非齐次Riemann-Hilbert边值问题的求解

doi:10.13371/j.cnki.chin.q.j.m.2024.03.004

数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 262-269.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.004

非齐次Riemann-Hilbert边值问题的求解

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

收稿日期:2023-11-14 出版日期:2024-09-30 发布日期:2024-09-30
通讯作者: ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; E-mail:z6483384940224@163.com
作者简介:ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; LI Ping-run (1966-), male, native of Yanzhou, Shandong, professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function, singular integral equation and Clifford analysis.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 11971015).

On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received:2023-11-14 Online:2024-09-30 Published:2024-09-30
Contact: ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; E-mail:z6483384940224@163.com
About author:ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; LI Ping-run (1966-), male, native of Yanzhou, Shandong, professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function, singular integral equation and Clifford analysis.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11971015).

摘要/Abstract

摘要： This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

关键词: Generalized Riemann-Hilbert problem, Uniformization theorem, Analytic solution, Sokhotski-Plemelj formula

Abstract: This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

Key words: Generalized Riemann-Hilbert problem, Uniformization theorem, Analytic solution, Sokhotski-Plemelj formula

中图分类号:

O174.5

张雯雯, 李平润. 非齐次Riemann-Hilbert边值问题的求解[J]. 数学季刊, 2024, 39(3): 262-269.

ZHANG Wen-wen, LI Ping-run. On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(3): 262-269.

非齐次Riemann-Hilbert边值问题的求解

On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems

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